A universal scaling law of intra-urban inequality

Large-scale urban agglomeration yields economic benefits but often coincides with pronounced environmental and social disparities. While aggregate urban attributes follow predictable scaling laws, how intra-urban inequality scales with city size remains unclear. To bridge this gap, we analyze over 11,000 global urban centers using multi-source satellite data to quantify inequalities in thermal exposure, green space, and economic activity. Here we show that all three dimensions follow super-linear scaling laws with city population size. Specifically, a doubling of city population is associated with an approximately 8-9% higher inequality Gini coefficient. Furthermore, these scaling relationships are significantly modulated by national socioeconomic development and background climate: green space and economic inequalities exhibit steeper scaling in low-income nations, whereas thermal inequality scales most acutely in arid climates. Consequently, achieving equitable urban development requires targeted interventions rather than relying on passive scale effects.